A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system

Generalized SAV approaches for gradient systems

(2021) Qing Cheng et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation

(2020) Xiaoli Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

A Positivity-Preserving Second-Order BDF Scheme for the Cahn-Hilliard Equation with Variable Interfacial Parameters

(2020) Lixiu Dong   Communications in Computational Physics

A new Lagrange multiplier approach for gradient flows

(2020) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation

(2019) Wenbin Chen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Energy stability and convergence of SAV block-centered finite difference method for gradient flows

(2019) Xiaoli Li et al.   MATHEMATICS OF COMPUTATION

Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation

(2019) Qi Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

(2019) Lianlei Lin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Third Order Exponential Time Differencing Numerical Scheme for No-Slope-Selection Epitaxial Thin Film Model with Energy Stability

(2019) Kelong Cheng et al.   JOURNAL OF SCIENTIFIC COMPUTING

Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation

(2019) Zhengguang Liu et al.   NUMERICAL ALGORITHMS

Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation

(2019) Zhengguang Liu et al.   APPLIED NUMERICAL MATHEMATICS

A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity

(2019) Zhiguo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation

(2018) Qiang Du et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach

(2018) Qing Cheng et al.   JOURNAL OF SCIENTIFIC COMPUTING

Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

(2017) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

(2017) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical Approximations for the Cahn–Hilliard Phase Field Model of the Binary Fluid-Surfactant System

(2017) Xiaofeng Yang   JOURNAL OF SCIENTIFIC COMPUTING

Unconditionally Energy Stable Linear Schemes for the Diffuse Interface Model with Peng–Robinson Equation of State

(2017) Hongwei Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Analysis and Approximation of a Fractional Cahn--Hilliard Equation

(2017) Mark Ainsworth et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

An $H^2$ convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn–Hilliard equation

(2016) Jing Guo et al.   Communications in Mathematical Sciences

Efficient and stable exponential time differencing Runge–Kutta methods for phase field elastic bending energy models

(2016) Xiaoqiang Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

First and second order numerical methods based on a new convex splitting for phase-field crystal equation

(2016) Jaemin Shin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends

(2016) Xiaofeng Yang   JOURNAL OF COMPUTATIONAL PHYSICS

Margination of white blood cells: a computational approach by a hydrodynamic phase field model

(2016) Wieland Marth et al.   JOURNAL OF FLUID MECHANICS

Efficient energy stable numerical schemes for a phase field moving contact line model

(2015) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects

(2015) Z. Guo et al.   JOURNAL OF FLUID MECHANICS

A review on phase-field models of brittle fracture and a new fast hybrid formulation

(2014) Marreddy Ambati et al.   COMPUTATIONAL MECHANICS

Second order convex splitting schemes for periodic nonlocal Cahn–Hilliard and Allen–Cahn equations

(2014) Zhen Guan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

(2013) A. Baskaran et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation

(2012) Zhengru Zhang et al.   Communications in Computational Physics

Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy

(2012) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

(2010) Christian Miehe et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

(2010) Jie Shen et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Phase-field-crystal model for fcc ordering

(2010) Kuo-An Wu et al.   PHYSICAL REVIEW E

Phase field crystal study of deformation and plasticity in nanocrystalline materials

(2009) Peter Stefanovic et al.   PHYSICAL REVIEW E